At some point you have to admit that for Danes, Danish lives are more valuable than non-Dane lives (same goes for every country). This isn't something that politicians can really say out loud, though, and the pro-refugee camp is milking it for all it's worth with the emotional appeals.
Okay, so a father and his child are at the border, what do you say to him? This is posed as a rhetorical question, the implication being that of course you help a fellow in need, yet the answer to that should be easy: you turn him away. It's a really small percentage of these refugees that are actual refugees, anyway, that actually have things really bad. Most of them had money to pay smugglers charging exorbitant fees.
So back to what I mentioned earlier, the lives of your own citizens is worth a lot more than the lives of anyone else, this is the unspoken truth. If this weren't the case, then governments would find the bare minimum living standard, force all their citizens to that, then give the left-over money to those truly in need in Africa, South America, the Middle East, etc. You know, the people actually dying of thirst and hunger, being forced to become child soldiers, sold to sex slavery, dying of disease... as opposed to, oh, I don't know, these healthy, well-fed young males streaming into Europe.
Things being as they are, i.e., citizens having more value than foreigners, the appeals to emotion should hold no weight in these discussions. It should be about the raw facts, the consequences, the crime rates- but of course, the pro-immigration camp only uses statistics like a drunkard uses a lamppost: for support, not for illumination. That is, when they, ever so rarely, choose to engage numbers and logic at all instead of sticking to their emotionally stirring imagery.
If you want to spend money to save human lives, taking these refugees is not the effective way of doing that. It isn't effective altruism.
Naturally, that means fuck-all to the general public. Humans tend to only care about what they can see or imagine. And there are so many biases in play, like scope insensitivity, and the fact that politicians deal with The Crowd, not individuals, and the crowd doesn't care about what makes sense and what doesn't. Gustav Le Bon wrote a pretty good book about that.